Circuit lower bounds from learning-theoretic approaches

An important open problem in computational complexity theory is to prove the size of circuits, namely, Boolean circuit lower bounds, necessary to solve explicit problems. We survey learning-theoretic approaches to proofs of Boolean circuit lower bounds in this paper. In particular, we discuss how to prove circuit lower bounds in uniform classes by assuming (or constructing) circuit-learning algorithms in several settings, such as the exact, probably approximately correct (PAC), and statistical query learning models.